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3 years ago

The sales tax on a used car priced at $4600 is $409.40. What is the sales tax rate?

Mathematics

1 answer:

Marina CMI [18]3 years ago

6 0

Answer:

8.9%

Step-by-step explanation:

sales tax rate (in percentage) = 409.40÷4600*100=8.9%

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Water is leaking out of an inverted conical tank at a rate of at the same time that water is being pumped into the tank at a con

Alexus [3.1K]

Water is leaking out of an inverted conical tank at a rate of 10,500 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank

<h3>Answer:</h3>

The rate at which water is being pumped into the tank is 289,752 $cm^3/min$

<h3>Solution:</h3>

According to question,

There is an inverted conical tank, through which water is leaking at a rate of 10,500 cm3/min at the same time that water is being pumped into the tank at a constant rate

The dimension of tank are:

Diameter = 4cm

Radius(r) = $\frac{diameter}{2}$ = 2cm

Height = 6cm

Clearly we can see that height is 3 times radius so, we can write

h = 3r OR r = h/3 ……………………. (1)

The volume of cone "V" is given as:

$\text { volume of cone }(\mathrm{V})=\frac{1}{3} \pi r^{2} h$ -------- (2)

From (1) and (2)

$\text { Volume of cone(V) }=\frac{1}{3} \pi\left(\frac{h}{3}\right)^{2} h$

$\mathrm{V}=\frac{\pi h^{3}}{27}$ -------- (3)

Now we calculate the derivate:-

$\frac{d V}{d t}=\frac{3 \pi h^{2}}{27} \frac{d h}{d t}$

$\frac{d V}{d t}=\frac{\pi h^{2}}{9} \frac{d h}{d t}$ --------- (4)

According to question, when height is 2m = 200cm, the water level is rising at a rate of 20 cm/min

$\frac{d h}{d t}=20 \mathrm{cm} / \mathrm{min}$

On putting above values in equation(4) and solving we get

$\frac{d V}{d t}=279252$

Hence, the rate at which water is being pumped is 289,752 $cm^3/min$ which is the sum of water volume increasing at rate of 279,252 and 10,500 leaking out

3 0

3 years ago

Amanda's jewelry box is in the shape a cube that has 6inches edges volume of Amanda's jewelry box?

Alona [7]

Volume = L x W x H

Length x Width x Height

6 times 6 times 6

216

7 0

3 years ago

Show that diagonal EG is a line of symmetry for rhombus EFGH. Н.

masha68 [24]

Dang that’s made hard srry i don’t know it just getting points

5 0

2 years ago

Need the answer showing work thank you.

fgiga [73]

Answer:

6 without repetition

27 with repetition

Step-by-step explanation:

without repetition, you have 3 digits to choose from initially, then only 2, then only one, i.e.:

3×2×1 = 6

with repetition, you have 3 digits to choose from for every spot:

3×3×3 = 27

4 0

2 years ago

There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious ap

Delvig [45]

Answer:

98% confidence interval is (-0.105 , 0.265)

Step-by-step explanation:

n1 = 75 n2 = 75

X1 = 48 X2 = 42

P1 = X1/N1 = 0.64 P2 = X2/N2 = 0.56

98% confidence interval for difference between two proportions is :

P1 - P2 + Z $\sqrt{P1 (1-P1)/n1 + P2 (1-P2)/n1}$

= 0.08 + 0.185

= (-0.105 , 0.265)

98% confidence interval is (-0.105 , 0.265)

4 0

2 years ago